Dirty old man having look around church (6)
I believe the answer is:
lecher
'dirty old man' is the definition.
(I've seen this in another clue)
'look around church' is the wordplay.
'look' becomes 'leer' (leer is a kind of look).
'around' indicates putting letters inside.
'church' becomes 'ch' (abbreviation on maps etc).
'leer' enclosing 'ch' is 'LECHER'.
'having' is the link.
(Other definitions for lecher that I've seen before include "Libertine" , "Person of unrestrained sexual desires" , "Promiscuous chap" , "He's obsessed with sex" .)